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  4. Energy of an electron in the second orbit of hydrogen atom is E and the energy of electron in 3rd orbit of He will be:

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Q. Energy of an electron in the second orbit of hydrogen atom is E and the energy of electron in 3rd orbit of He will be:

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Solution:

The energy for nth orbit in the atom of atomic number (Z) is given by $ {{E}_{n}}=\frac{{{Z}^{2}}}{{{n}^{2}}}{{E}_{0}} $ So, for helium (Z = 2) and n = 3 $ \therefore $ for third orbit $ {{E}_{3}}=\frac{4}{9}{{E}_{0}} $ ?(1) Now for H atom (Z = 1) and n = 2 $ \therefore $ for second orbit $ {{E}_{2}}=\frac{1}{4}{{E}_{0}} $ ?(2) Now from Eqs. (1) and (2), we obtain $ \frac{{{E}_{3}}}{{{E}_{2}}}=\frac{\frac{4}{9}{{\varepsilon }_{0}}}{\frac{1}{4}{{E}_{0}}}=\frac{16}{9} $ or $ {{E}_{3}}=\frac{16}{9}{{E}_{2}}=\frac{16}{9}E $